Page 26 - Algebra 1

Types of function
• One to one function
A function f: X → Y is one to one when an element x1 of X is associated to x2 which is a unique element of B.
f(x1) = f (x2)
⟹ x1 = x2
For example, f (x) = x3
f(2)=23 =8
f(–2) = (–23) = –8
2 and –2 has a different image. So, this is a one-to-one function.
• Many to one function
A function f : X → Y is one to one when two or more elements x1, x2.... of X are associated with an element of Y.
For example, f (x) = x2
f(2)=22 =4
f(–2) = (–22) = 4
2 and –2 has a different image. So, this is a many-to-one function.
Some special types of function
• Inverse function
For every function y = f(x), the inverse of the function is given by x = f-1(y)
• Even and odd function
If f(x) is a function of x such that f(-x) = f(x), then f(x) is an even function. For example, f(x) = x2 – 2, f(–x) = (–x)2 – 2
f(–x)=x2 –2
So, f(x) = f(–x), so it’s an even function.
If f(x) is a function of x such that f(x) = – f(x), then f(x) is an odd function. For example, f(x) = x3 + 2x, f(–x) = (–x)3 + 2(– x)
f(–x) = (–x3 –2x)
So, f(x) = –f(x), so it’s an odd function.
• Constant function
If f(x) = c for all x € R, then f(x) is a constant function. For example, f(x) = 12 is a constant function.
• Modulus function
f(x)=|x|for(𝑥, 𝑥≥0) –x, x<0
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ALGEBRA